How do I make an automatic tail that is bone rigged?
[Updated]
Simplest tail rig ever possible.
The tail has 8 bones the last bone is its tip.
In pose mode.
Adjust all influence to about .5
Add a bone constraint to the 6th bone "track to" the 8th bone. 
Add a bone constraint to the 4th bone "track to" the 6th bone. 
Add a bone constraint to the 2d bone "track to" the 4th bone. 

Done.